Mathematical Ideas that Shaped the World

This week marked the end of a new venture for me: designing and teaching a course for adults to learn about some of the big ideas in maths: their history, impact and philosophy. At the beginning of this post I have to thank Stephan Matthiesen for helping me to plan and give 3 of the lectures while I was so busy with my thesis; without him the course would surely never have come to pass.

The University of Edinburgh runs a wonderful scheme called Open Studies, which is a set of adult-learning courses on all manner of subjects, from Ancient Botany to Victorian Fairy Painting; from Shakespeare’s Villains to Parapsychology; from the Science of Attraction to Forensic Medicine. Some of the courses are for credit, i.e. can be put towards a qualification, while others are taken completely for fun.

It was while taking the course on Scottish Philosophy that I realised that there was both a need for and a lack of a mathematics course. In every week’s class, mathematics came up in some context of the history of philosophy (for example, the invention of non-Euclidean geometry challenging the concept of absolute truth), yet both the teacher and students knew very little about the topics being discussed. If these ideas were so important, didn’t they deserve a course of their own?

It was a year in the planning, but finally in January I was ready to welcome my new class to learn about Mathematical Ideas that Shaped the World. Since the course was at 2pm on a Tuesday, the majority of the students were retired, and strangely enough the majority seemed to have a background in either chemical engineering or the civil service. We also had one forensic anthropologist and one law student to round out the numbers. Their backgrounds were very mixed, with some having done a University course in maths or science, and others not having done any maths since an O-Level 30 years ago. But they were all enthusiastic and willing to learn, which is all a teacher can ask of a class.

Count Sheepula

If you want to see the syllabus for the course you can look at the course website (which incidentally also contains a good list of links to maths in the BBC and wider media). I tried to choose topics which were the biggest mathematical ‘discoveries’ of the last few centuries and which have had the biggest impact on history and philosophy. My favourite lectures were Lecture 3 about the different sizes of infinity (probably the most mind-boggling!) and Lecture 7 about non-Euclidean geometry (probably the most fun, with drawing on balloons and cutting up Möbius strips). With a bit of cunning, I also managed to sneak Vlad into Lecture 5 as Count Sheepula trying to solve the Königsberg bridges problem.

There were lots of interesting questions and comments through the course, but the most memorable for me was a debate on whether 0.999… = 1. At the beginning of the lecture all of the students unanimously agreed that the two numbers were not equal, and even after my best mathematical arguments I’m not sure I managed to convince anyone otherwise. This has also been true of every non-mathematician I’ve talked to since then! Almost everyone will say that 0.999… approaches 1 but never actually reaches it – it’s always slightly smaller than 1. To believe that the two numbers are equal requires a deep understanding of the nature of infinity, and even some mathematicians disagree on this. The concept is such a misunderstood one that a whole Wikipedia article is dedicated to it. Try reading the arguments and see if you can be convinced!

A mathematical way to cut a bagel in half

I was sad to have to give the last lecture of the course this week but I’m glad to have had such a fun time in giving it and such stimulating conversations along the way. To finish off the course in style, Stephan and I hosted a ‘maths picnic’ where everyone was asked to bring in some food that represented some maths they’d learnt about in the course. My contribution was to bring in some bagels and teach people a way to cut the bagel in half in such a way that the two halves are linked together. (See George Hart’s website for instructions!) I was delighted by the effort that the other students went to to buy or make mathematical food – you can see the whole range on the website – but special mention has to go to the ladies who made the ‘Normal Distribution cake’ and the set of mathematical cupcakes (one for each week of the course!). For my benefit we even had a sheep-themed tablecloth!

If any of my students are reading this, I’d like to thank them again for being so enthusiastic for the whole 10 weeks and for making my job so enjoyable. If any Edinburgh residents are reading who didn’t get to come to the course, then don’t worry – I’m giving it again twice next year, and at different times too! Finally, if any science communicators are reading, I hope that my success in the course will inspire them to teach similar courses in other cities. There is definitely a market for it (the course was over-subscribed) and I think it is important to teach people the part that mathematical ideas have played in shaping the history of the world.

It *was* a rally great course! And it is indeed brilliant that it’s back next year as I sadly had to miss quite a few classes and intend taking it again to ‘re-sit’ the sessions I missed.
Julia’s excellent at Engaging with her public, and we were a fairly mixed batch of students, I would say. She pitched the level pretty well, from the start to the end, and made us understand why she was so enthusiastic!
(and yes, that’s going into the Feedback!)

Ooh thanks for providing some more details on this and the links to the syllabus and bagel instructions (I will have to try that). Could you make the links open in a new window? Well done on a successful course.